Police were called after at least four teenagers returned from an Edinburgh Academy Easter cadet camp covered from head to toe in bruises.
The 15-year-old victims told their horrified parents they had been restrained and then thrashed by older students.
The £11,000-a-year school, which was founded by Sir Walter Scott and counts Robert Louis Stevenson among its former pupils, has army and air sections in a Combined Cadet Force.
A group of army cadets from the school is understood to have travelled to an outdoor activities centre near Aberdeen during the holiday.
An insider said: "When the boys and girls came back from their trip, at least four parents said their children were covered head to toe in bruises.
"The kids told them that they had been tied up before being kicked and punched.
"They were whipping the younger boys with wire coat hangers."
The insider added: "They didn't know if it was an initiation of sorts or having 'fun' but now the parents want criminal charges brought against these bullies.
"You don't expect to send your children away on a school trip for them to come back hurt and upset.
"We've no ideas where the teachers were when this was happening."
The school's web site says the "self-run Adventurous Training/Military camp" is "always very popular amongst the cadets".
Activities usually include camping, orienteering, hill-walking, self-reliance and leadership skills.
The Easter camp is one of two events for the Army Section of the Combined Cadet Force in a year.
Edinburgh Academy, which has produced nine recipients of the Victoria Cross, sets out on its website the high standards expected of all students.
"We expect that Academy pupils will recognise the need to behave in a way which graces the school wherever they are," it states.
"The rector reserves the right to investigate and take action on reports of unlawful, violent or indecent behaviour by a pupil or behaviour which damages the reputation of the school even if such behaviour takes place outwith school time or school premises."
An Edinburgh Academy spokesman said: "The school takes its duty of care towards pupils very seriously.
"An internal investigation into alleged incidents between pupils from the school at a camp during the Easter break is under way."
Police Scotland yesterday confirmed that it had been notified of the incident and was making enquiries.
A police spokesman said: "Officers in Edinburgh are carrying out initial enquiries following reports of assaults involving pupils from a school within the capital.
"We are liaising closely with the school at this time to determine the most appropriate course of action."
Cadet trips from Edinburgh Academy are legally considered school outings and all participants are warned that they face expulsion for serious breaches of the rules.
Cadets on the Easter trip were told: "Initiation ceremonies/games/dares are completely unacceptable and any involvement in, or suggestion of, such activity will result in very serious sanction.
"Anyone who takes part in any bullying or inappropriate behaviour risks being expelled from the school."